What you say is false. A person can start a fight with force of violence. They are guilty of a crime, yes, but they don't forfeit the right to save their own hide if the other person escalates it to a fight to the death.
The felony provision has to be a felony independent of the fight. There is a ton of case law on that point.
-- Otherwise, if a perp attempted to mug an innocent citizen, then won the ensuing gun fight, he could claim self-defense and walk. --
That is false too. The person who initiates force (or threatens force) is a criminal, period. The mugger does not get off.
Which is exactly what I said in the first case. Assault is a felony, too. If what you say is true, muggers can't claim self-defense, but just plain old attackers (rapists) can.
776.041 Use of force by aggressor.—The justification described in the preceding sections of this chapter is not available to a person who:
(1) Is attempting to commit, committing, or escaping after the commission of, a forcible felony; or
(2) Initially provokes the use of force against himself or herself, unless:
(a) Such force is so great that the person reasonably believes that he or she is in imminent danger of death or great bodily harm and that he or she has exhausted every reasonable means to escape such danger other than the use of force which is likely to cause death or great bodily harm to the assailant; or
(b) In good faith, the person withdraws from physical contact with the assailant and indicates clearly to the assailant that he or she desires to withdraw and terminate the use of force, but the assailant continues or resumes the use of force.
IOW, if you started the fight, the “duty to retreat” pops back up.